On the worst-case disturbance of minimax optimal control

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We consider a minimax optimal control problem for uncertain stochastic systems. The uncertainty in the underlying stochastic system is formulated in terms of probability measure perturbations satisfying a relative entropy constraint. By characterizing the worst-case measure for a related stochastic minimax game, it is shown that the worst-case uncertain system can be represented in the form of a parametric perturbation of the nominal system. A numerical example is presented to illustrate theoretical results developed in this paper.